- #1
Wminus
- 173
- 29
Hi!
While testing my knowledge of analytical mechanics I stumbled across a fallacy that I am unable to resolve. Could you assist me?
When you finish integrating a Lagrangian over the time domain ##[t_1,t_2]##, shouldn't its position ##q(t)## and position dot ##\dot{q(t)}## variables take the values of ##q(t_2),q(t_1),\dot{q(t_1)},\dot{q(t_2)}##? Hence the action integral is just a function of the endpoints, and since the variation at the endpoints is zero the action integral should be zero for ALL parametrization of ##q## and ##\dot{q}##.
So have I found a glaring flaw in the theory of physics? :P Or is there something I am missing?
thanks for all input :)
While testing my knowledge of analytical mechanics I stumbled across a fallacy that I am unable to resolve. Could you assist me?
When you finish integrating a Lagrangian over the time domain ##[t_1,t_2]##, shouldn't its position ##q(t)## and position dot ##\dot{q(t)}## variables take the values of ##q(t_2),q(t_1),\dot{q(t_1)},\dot{q(t_2)}##? Hence the action integral is just a function of the endpoints, and since the variation at the endpoints is zero the action integral should be zero for ALL parametrization of ##q## and ##\dot{q}##.
So have I found a glaring flaw in the theory of physics? :P Or is there something I am missing?
thanks for all input :)